But Conservatives opposing the reforms warned that the fight against the move had only just begun and warned it could undermine the Prime Minister’s leadership.

Several angrily accused Cabinet Office Minister Francis Maude of a “sneering” tone towards them in a “jaw-dropping” TV interview.

The Marriage (Same Sex Couples) Bill passed its first Parliamentary hurdle in a free vote on Tuesday night after an often passionate debate. But it faces further scrutiny by MPs before going to the Lords.

It got its Second Reading by 400 votes to 175 with the help of most Labour and Lib Dem MPs. But it split the Tory party, with 136 of Mr Cameron’s 303 troops voting against it, including two Cabinet ministers.

Forty more Tories did not vote or officially abstained. Just 127, including Mr Cameron, endorsed the proposal.

If passed, it will let gay couples in England and Wales marry in civil or religious ceremonies, where churches “opt in”.

Mr Cameron told the Commons the Bill would boost marriage and society.

He rebuffed a suggestion by senior Tory Christopher Chope, who voted against the Bill, for straight couples to be given equal rights with gay people to be allowed civil partnerships.

Mr Cameron told him: “Frankly, I am a marriage man. I am a great supporter of marriage. I want to promote marriage, defend marriage, encourage marriage.

“The great thing about last night’s vote is that two gay people who love each other will now be able to get married and I think that is an important advance.” But Tory backbencher Stewart Jackson predicted the vote would have a significant impact on Mr Cameron’s leadership.

He said: “The only comparable rebellion is the Iraq war vote in 2003 which undermined Blair’s Premiership. This vote will do the same for Cameron.”

Chairman of the backbench 1922 committee Graham Brady said he had “serious misgivings” over assurances on religious freedom while former defence minister Sir Gerald Howarth said the Government had no mandate for such a “massive social and cultural change”. But Labour MP Diane Abbott said the vote proved “the arc of history bends slowly but it bends towards justice”.

He said many Conservatives were “completely relaxed” about gay marriage and predicted many opponents would come round to the idea. “Sometimes parts of the Conservative party move a few paces behind prevailing social attitudes...but we get there, maybe at different speeds,” he said.

But one Tory said: “I watched Maude on Newsnight and my jaw nearly hit the floor. He wasn’t even bothering to disguise the contempt in which he holds the viewpoint of most of the party.”

Another said: “This kind of sneering towards party members against gay marriage is counterproductive.”

Mr Cameron’s official spokesman stressed it had been a free vote and the PM “very much respects the opinions of others”.